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The most commonly used techniques to generate a sequence of pseudorandom numbers are those that apply some form of recursive computation. In principle, such recursive formulas are based on calculating the residuals modulo of some integers of a linear transformation. The process of producing a random number sequence is completely deterministic. However, the generated sequence […]

As noted previously, the accuracy of the model output statistics and probabil­ity distribution (e. g., probability that a specified safety level will be exceeded) obtained from Monte Carlo simulation is a function of the number of simu­lations performed. For models or problems with a large number of uncertain basic variables and for which low probabilities […]

6.1 Introduction As uncertainty and reliability related issues are becoming more critical in en­gineering design and analysis, proper assessment of the probabilistic behavior of an engineering system is essential. The true distribution for the system response subject to parameter uncertainty should be derived, if possible. How­ever, owing to the complexity of physical systems and mathematical […]

Determination of the availability or unavailability of a system requires a full accounting ofthe failure and repair processes. The basic elements that describe such processes are the failure density function ft (t) and the repair density func­tion gt (t). In this section computation of the availability of a single component or system is described under […]

5.4.1 Terminology A repairable system experiences a repetition of the repair-to-failure and failure — to-repair processes during its service life. Hence the probability that a system is in an operating condition at any given time t for a repairable system is different from that for a nonrepairable system. The term availability A(t) generally isused for […]

There are two basic categories of maintenance: corrective maintenance and preventive maintenance. Corrective maintenance is performed when the sys­tem experiences in-service failures. Corrective maintenance often involves the needed repair, adjustment, and replacement to restore the failed system back to its normal operating condition. Therefore, corrective maintenance can be regarded as repair, and its stochastic characteristics […]

The repair rate r (t), similar to the failure rate, is the conditional probability that the system is repaired per unit time given that the system failed at time zero and is still not repaired at time t. The quantity r (t) dt is the probability that the system is repaired during the time interval […]

Like the time to failure, the random time to repair (TTR) has the repair density function gt (t) describing the random characteristics of the time required to re­pair a failed system when the failure occurs at time zero. The repair probability Gt(t) is the probability that the failed system can be restored within a given […]

For repairable hydrosystems, such as pipe networks, pump stations, and storm runoff drainage structures, failed components within the system can be re­paired or replaced so that the system can be put back into service. The time required to have the failed system repaired is uncertain, and consequently, the total time required to restore the system […]

In general, the reliability of a system or a component is strongly dependent on its age. In other words, the probability that a system can be operational to perform its intended function satisfactorily is conditioned by its age. This conditional reliability can be expressed mathematically as P(TTF > t, TTF > t + M)P(TTF > […]